rubilia/NormalValues

Sub-page of Rubilia

Table of contents Table of diagrams
(0.00, 0.00)
(-1.50, 0.50)
(-1.00, 0.50)
(-1.00, 0.50)
(-4.00, 0.50)
(0.50, 0.50)
(0.33, 0.67)
(0.67, 0.67)
(0.33, 0.67)
(0.33, 0.67)
(0.33, 0.67)
(0.33, 0.67)
(-0.75, 0.75)
(-0.25, 0.75)
(-0.25, 0.75)
(-1.17, 0.83)
(-0.33, 0.83)
(-0.33, 0.83)
(-1.17, 0.83)
(-0.33, 0.83)
(-0.33, 0.83)
(0.00, 1.00)
(-2.00, 1.00)
(1.33, 1.33)
(0.00, 1.00)
(1.00, 1.67)
(-0.40, 1.20)
(0.80, 1.80)
(-1.00, 1.00)
(-2.00, 1.00)
(0.00, 2.00)
(-1.00, 3.00)
(-3.00, 1.00)
(-3.00, 2.00)
(-5.50, 1.50)
(-7.00, 3.00)
(-8.00, 1.00)
(-9.00, 2.00)
Jump to take potential point
Defend potential point
Take away potential point
Take away potential point
Defend potential point
Under the stones sacrifice
Prevent sacrifice
Real half-point ko, B komaster
Real half-point ko, B komaster
Take away potential point, set up ko capture
Defend potential point, set up ko capture
Take stone to set up ko
Make ko
Take two stones
Take away territory (i)
Take away territory (ii)
Take three stones
Take away potential point (corridor)
Defend potential point, set up 0.67 position
Take away potential point
Sente
Reverse Sente
Protect, threaten 0.67 play
Take away potential point (corridor)
One more number
Take away potential point
Take away potential point (corridor)
Take away potential point (corridor)

Introduction

I am going to translate this copy of Miai values list to reduced chinese value vectors, which I'd like to call "normal values". I don't know if it's interesting to others, but to me, japanese mean and miai values are a little awkward to handle, since I am used to (and prefer) chinese scoring.



The structure of a normal value N is


N (T) = (S, U)


where

S - "score"
is the chinese [10] mean value of the current position, as compared to "zero",
U - "urgency"
is the chinese [10] miai value [11] of the current position, and
T - "tenuki value"
is the gain currently feasible by playing elsewhere [12].



Note: Like in common miai counting, it's assumed that

  1. there is no absent (super)ko
  2. the tenuki value is sufficiently stable
  3. there is a large number of alternative plays at any given tenuki value.

[10] referring to board points (子 "zĭ" - literally "stones"). At the end of the game, each point of the board counts to the color which is agreed to have conquered it.

[11] This is kind of an etymological oxymoron. Should it better be called "jiàn hé value"? Anyway, "urgency" refers to the locally biggest plays, regardless of (super)ko restrictions.

[12] I don't really like the term temperature, unfortunately regularly used in combinatory game theory, because the inherently stressed analogy to thermodynamical temperature is pronouncedly superficial.


Conventions

Note: In mathematical Go, colors are often treated inversly.

The list below shows the normal values N(T) = (S, U) for T = U, ordered by increasing U.

Beside each diagram you can see the underlying tree of normal values. Steps to the left are White's optimal moves, steps to the right are Black's. In ko situations, covering move alternatives are given, too. Double edges (or triple, where needed) are "forced" answers, being more urgent than the preceding move. Equal values of similar positions may be merged.

Linking to the relevant followers is a nice idea, but much work, so I'll do that later.


Reference Section

0.00


[Diagram]

(0.00, 0.00)

         (0, 0)
        /      \
  (0, 0)        (0, 0)

Of course, this makes sense only with single-stone self-capture allowed (equivalent to passing).


0.50


[Diagram]

(-1.50, 0.50)

           (-3/2, 1/2)
          /          \
    (-1, 0)            (-2, 0)

A single shared point.

[Diagram]

(-1.00, 0.50)

                                (-1, 1/2)
                               /         \
         (1/3, 2/3)__(-1/3, 2/3)            (-3/2, 1/2)
       //                       \\         /           \
 (1, 0)                            (-1, 0)              (-2, 0)

w can be regarded as 100% white, and unlike in a ko situation, not just b but also BC as 100% black.



[Diagram]

(-1.00, 0.50)

                                    (-1, 1/2)
                                   /         \
                             (0, 1)            (-3/2, 1/2)
                            /      \\        /            \
                    (1, 1/2)         (-1, 0)               (-2, 0)
                   /        \
         (3/2, 1/2)          (1/3, 2/3)__(-1/3, 2/3)
        /          \       //                       \
  (2, 0)             (1, 0)                          (-1, 0)

w is fully white, and BC fully black again, no matter how many b points there are (which also count entirely to Black, of course).

[Diagram]

(-4.00, 0.50)

                                        (-4, 1/2)
                                       /         \
                            (-3/2, 5/2)           (-9/2, 1/2)
                           /           \\         /           \
                   (1, 1/2)               (-4, 0)              (-5, 0)


In situations like this and the previous one, with exactly one w, and at least one BC and one b point each,



[Diagram]

(0.50, 0.50)

                                    (1/2, 1/2)
                                   /          \
                           (1, 1/2)             (-7/4, 9/4)
                          /        \          //           \
                (3/2, 1/2)          (1/2, 1/2)              (-4, 0)
               /          \        /          \
         (2, 0)             (1, 0)             (0, 0)

Only 1½ of the 6 unsettled points belong to Black, here, but Black has a valuable ko threat. If Black doesn't use it until the late endgame stage, the capture by White is equivalent to taking a shared point.




0.67


ko

[Diagram]

(0.33, 0.67)

         (1/3, 2/3)__(-1/3, 2/3)
        /                       \
  (1, 0)                         (-1, 0)

Black has 2/3 points equity in WC. We may think of it as 2/3 captured. The remainder is the mean value 1/3 ≈ 0.33 to White's favor (hence positive).



Hidden ko

[Diagram]

(0.67, 0.67)

                         (2/3, 2/3)
                        /          \
              (4/3, 2/3)            (-2/3, 4/3)
                        \          //           \
             (4/3, 2/3)__(2/3, 2/3)              (-2, 0)
            /                      \
      (1, 0)                        (-1, 0)

We may think of the two marked points as 2/3 conquered by Black each. The 0.67 mean value results from the remaining third parts of them: 2 * (1/3) = 2/3 ≈ 0.67.



[Diagram]

(0.33, 0.67)

                                 (1/3, 2/3)
                                /          \
                              /              \
                            /                  \
                   (1, 1/2)                      \
                  /        \                       \
        (5/2, 3/2)          (1/2, 1/2)               \
       /          \\      /           \                \
 (4, 0)             (1, 0)             (0, 0)           (?, ?)
                                                      //      \
                              (13/6, 11/6)__(1/3, 2/3)         (?, ?)
                             /           \\           \
                       (4, 0)              (1/3, 2/3)__(-1/3, 2/3)
                                          /                       \
                                    (1, 0)                         (-1, 0)



[Diagram]

(0.33, 0.67)

        ............(19/9, 8/9)__(11/9, 8/9)__(1/3, 2/3)
       /                        /           \\          \
 (3, 0)   (7/3, 2/3)__(5/3, 2/3)              (1/3, 2/3)__(-1/3, 2/3)
         /                       \          /                        \
   (3, 0)                           (1, 0)                            (-1, 0)



[Diagram]

(0.33, 0.67)

                   (5/3, 4/3)__(1/3, 2/3)
                  /          \\          \
            (3, 0)             (1/3, 2/3)__(-1/3, 2/3)
                              /                       \
                        (1, 0)                         (-1, 0)



[Diagram]

(0.33, 0.67)

                             (1/3, 2/3)
                            /          \
                    (1, 1/2)             (-1/3, 2/3)
                                        /           \
                  (5/3, 4/3)__(1/3, 2/3)             (-7/6, 5/6)
                 /          \\          \           //          \
           (3, 0)             (1/3, 2/3)__(-1/3, 2/3)           //
                             /                       \          \\
                       (1, 0)                         (-1, 0)     (-2,0)

Black at a starts a ko, White at a prevents it.

The previous situation is a follower of this one, which is why its tree is a subtree here - look for the "asymmetric ko" line

 (5/3, 4/3)__(1/3, 2/3)

and below.


0.75


[Diagram]

(-0.75, 0.75)

                  (-3/4, 3/4)
                 /           \
           (0, 0)             (-3/2, 1/2)

Defend or take away potential single-point eye.

Currently, x can be referred to as 1/4 white, 3/4 black.



[Diagram]

(-0.25, 0.75)

                  (-1/4, 3/4)
                 /           \
       (1/2, 1/2)             (-1, 1/2)

Either player starting at x.

Here, x can be referred to as 3/4 white, 1/4 black.

[Diagram]

(-0.25, 0.75)

                  (-1/4, 3/4)
                 /           \
       (1/2, 1/2)             (-1, 1)
                             //      \
                        (0, 1)        (-2, 0)
                       /     \\
                 (1, 0)       (-1, 1/2)

As can be seen, the marked white stone doesn't affect the value. Still, x is 3/4 white, 1/4 black.


work in progress


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0.83



[Diagram]

(-1.17, 0.83)

                                .....(-7/6, 5/6).....
                               /                     \
        (1/3, 2/3)__(-1/3, 2/3)                       (-2, 1/2)
       /                       \                     /        \
 (1, 0)                         (-1, 0)       (-1, 1)          (-5/2, 1/2)
                                              /      \\
                                        (0, 1)        (-2, 0)
                                       /     \\
                                 (1, 0)       (-1, 1/2)

BC completely belongs to Black, and even x is 1/6 black.

[Diagram]

(-0.33, 0.83)

                                (-1/3, 5/6)
                               /           \
                     (1/2, 1/2)             (-7/6, 5/6)

x can be referred to as 2/3 white, 1/3 black.

[Diagram]

(-0.33, 0.83)

                                (-1/3, 5/6)
                               /           \
                     (1/2, 1/2)             (-37/24, 35/24)
                                           //              \
                              (-1/12, 13/12)                (-3, 0)
                             /             \\
                       (1, 0)                (-7/6, 5/6)

As can be seen, the marked stones don't affect the value. Still, x is 2/3 white, 1/3 black.



[Diagram]

(-1.17, 0.83)

                                ...(-7/6, 5/6)...
                               /                 \
        (1/3, 2/3)__(-1/3, 2/3)                   (-2, 1)....
       /                       \                 //          \
 (1, 0)                         (-1, 0)    (-1, 1)            (-3, 1/2)
                                          /      \\          /         \
                                    (0, 1)        (-2, 0)   |           (-7/2, 1/2)
                                   /      \                 \\
                             (1, 0)        (-1, 1/2)         (-3, 0)

BC completely belongs to Black, and even x is 1/6 black.



[Diagram]

(-0.33, 0.83)

                                (-1/3, 5/6)
                               /           \
                     (1/2, 1/2)             (-7/6, 5/6)

x can be referred to as 2/3 white, 1/3 black.



[Diagram]

(-0.33, 0.83)

                                (-1/3, 5/6)
                               /           \
                     (1/2, 1/2)             (-49/24, 47/24)
                                           //              \
                              (-1/12, 13/12)                (-4, 0)
                             /             \\
                       (1, 0)                (-7/6, 5/6)

As we can see again, the marked stones don't affect the value. Still, x is 2/3 white, 1/3 black.



1.00



[Diagram]

(0.00, 1.00)

                      (0, 1)
                     /      \
             (1, 1/2)        (-1, 1)
                            /       \
                      (0, 1)         (-2, 1/2)
                     /      \
             (1, 1/2)        (-1, 0)




[Diagram]

(-2.00, 1.00)

                      ..(-2, 1)..
                     /           \
          (-1/2, 3/2)             (-3, 1)...
         /          \\           /          \
 (1, 1/2)            (-2, 0)    |            (-4, 1/2)
                                \\          /         \
                                 (-3, 0)   |           (-9/2, 1/2)
                                           \\
                                            (-4, 0)


In situations like this and the previous one, with at least two w and b points each,




Unsecured ko

[Diagram]

(1.33, 1.33)

         (4/3, 4/3)
        /          \
       |            (0, 0)
       \\
        (4/3, 2/3)

The (4/3, 2/3) result represents the plain (secured) ko after white captured and black countered.



Elementary two-step ko

[Diagram]

(0.00, 1.00)

            ...............(1, 1)__(0, 1)__(-1, 1)................
           /                      /      \                        \
         /..(4/3, 2/3)__(2/3, 2/3)        (-2/3, 2/3)__(-4/3, 2/3)..\
       /                          \      /                            \
 (2, 0)                            (0, 0)                              (-2, 0)



Unsecured two-step ko

[Diagram]

(1.00, 1.67)

            ......(1, 5/3)__(-2/3, 4/3)...........
          /              \\                       \
         |                (-2/3, 2/3)__(-4/3, 2/3)..\
         \\              /                            \
          (1, 1)   (0, 0)                              (-2, 0)

The (1, 1) result represents the elementary (secured) two-step ko, where black blocked after the second white capture.



Elementary three-step ko

[Diagram]

(-0.40, 1.20)

        (4/5, 6/5)__(-2/5, 6/5)__(-8/5, 6/5)__(-14/5, 6/5)
       /           /           \/           \            \
 (2, 0)  (2/3, 2/3)      (-1, 1)(-1, 1)      (-8/3, 2/3)  (-4, 0)



Unsecured three-step ko

[Diagram]

(0.80, 1.80)

           .........(4/5, 9/5)__(-1, 5/3)__(-8/3, 4/3)
          /                  \\/        \\            \
         |                   / \\        (-8/3, 2/3)   (-4, 0)
         \\       (-2/3, 4/3)   (-1, 1)
          (4/5, 6/5)

The (4/5, 6/5) represents the elementary (secured) three-step ko with black having blocked after the third white capture.



[Diagram]

(-1.00, 1.00)

                               (-1, 1)
                              /       \
          (2, 5/3)__(1/3, 4/3)         (-2, 0)
          /      \\          \\
         |        (1/3, 2/3)  (-1, 0)
         \\
           (2, 1)



[Diagram]

(-2.00, 1.00)

                    .......(-2, 1).......
                   /                     \
            (-1, 1)                       |
           /       \                     //
 (1/3, 4/3)         (-2, 0)    (-5/3, 4/3)
                                         \\
                                          (-3, 0)



Second line mutual atari

[Diagram]

(0.00, 2.00)

                    (0, 2)
                   /      \
             (2, 1)        (-2, 1)



Second line mutual atari, one side uncovered

[Diagram]

(-1.00, 3.00)

                    (-1, 3)
                   /       \
             (2, 1)         |
                           //
                     (-1, 1)



2 vs. 1 on the second line

[Diagram]

(-3.00, 1.00)

                    (-3, 1)
                   /       \
                  |         (-4, 1)
                  \\       /       \
                  (-3, 1/2)         |
                                   //
                            (-4, 1)
                           /       \
                  (-3, 1/2)         (-5, 0)



2 vs. 1 on the second line, uncovered

[Diagram]

(-3.00, 2.00)

                    (-3, 2)
                   /       \
                  |         (-5, 2)
                  \\       /       \
                  (-3, 1/2)         |
                                   //
                            (-5, 2)
                           /       \
                  (-3, 1/2)         |
                                   //
                            (-5, 0)



3 vs. 1 on the second line

[Diagram]

(-5.50, 1.50)

                .............(-11/2, 3/2).............
               /                                      \
       (-4, 1)                                         |
      /        \                                      //
     |          (-5, 1)                    (-11/2, 3/2)
     \\        /       \                  /            \
      (-4, 1/2)         |        (-4, 5/6)              (-7, 0)
                       //       /         \
                (-5, 0)        |           (-29/6, 5/6)
                               \\         /            \
                                 (-4, 1/2)              (-17/3, 2/3)



3 vs. 1 on the second line, uncovered

[Diagram]

(-7.00, 3.00)

                ...............(-7, 3)...............
               /                                     \
       (-4, 1)                                        |
      /        \                                     //
     |          (-5, 1)                  ......(-7, 3)......
     \\        /       \                /                   \
      (-4, 1/2)         |        (-4, 1)                     |
                       //       /        \                  //
                (-5, 0)        |          (-5, 1)     (-7, 0)
                               \\        /       \
                                (-4, 1/2)         |
                                                 //
                                          (-5, 0)



4 vs. 1 on the second line

[Diagram]

(-8.00, 1.00)

                          ..........(-8, 1).........
                         /                           \
           ..(-20/3, 5/3)..                           |
          /               \\                          :
   (-5, 1)                 (-25/3, 4/3)               :
  /       \               //          \               :
 |        (-6, 1)   (-7, 0)            |              :
 \\       /     \                    //              //
  (-5, 1/2)      |        (-25/3, 2/3)    (-23/3, 4/3)
                //                        /          \\
          (-6, 0)              (-19/3, 4/3)           (-9, 0)
                               /          \
                         (-5, 1)          (-23/3, 2/3)
                        /       \
                       |         (-6, 1)
                       \\       /       \
                        (-5, 1/2)       (-7, 1)



4 vs. 1 on the second line, uncovered

[Diagram]

(-9.00, 2.00)

                      ................(-9, 2).............
                     /                                    \
           ...(-7, 2)....                                  |
          /              \                                //
   (-5, 1)                |                 ......(-9, 7/3)......
  /       \              //                /                    \\
 |        (-6, 1)  (-7, 0)    .(-20/3, 5/3).                     |
 \\       /     \            /              \                  ///
  (-5, 1/2)      |    (-5, 1)               (-25/3, 4/3)  (-9, 0)
                //   /       \              /          \
         (-6, 0)    |        (-6, 1)  (-7, 0)           |
                    \\       /     \                   //
                     (-5, 1/2)     (-7, 1)  (-25/3, 2/3)




                ...............(-7, 3)...............
               /                                     \
       (-5, 1)                                        |
      /        \                                     //
     |          (-6, 1)                  ......(-7, 2)......
     \\        /       \                /                   \
      (-5, 1/2)         |        (-5, 1)                     |
                       //       /        \                  //
                (-6, 0)        |          (-6, 1)     (-7, 0)
                               \\        /       \
                                (-5, 1/2)         |
                                                 //
                                          (-6, 0)
                .......(-7, 3).......
               /                     \
       (-4, 1)                        |
      /        \                     //
     |          (-5, 1)       (-7, 3)
     \\        /       \             \
      (-4, 1/2)         |             |
                       //            //
                (-5, 0)       (-7, 0)
                .......(-5, 1)........
               /                      \
        (-4, 1)        ................(-6, 1).......
      /        \       /                             \
     |          (-5, 1)                               |
     \\        /       \                             //
      (-4, 1/2)         |              (-71/12, 13/12)
                       //             /              \\
                (-5, 0)    (-29/6, 5/6)                (-7, 0)
                         /            \
                (-4, 1/2)              (-17/3, 2/3)




quarry

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 O§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§§



[Diagram]

Jump to take potential point

Initial count: -3.5

[Diagram]

Defend potential point

Initial count: 2.5

[Diagram]

Take away potential point



[Diagram]

Take away potential point

Initial count: -0.5

[Diagram]

Defend potential point



[Diagram]

Under the stones sacrifice

Initial count: -2.5

After W3 the corner is worth -2. Black has captured 3 White stones, but White can claim the B2 stone.

(Note: If Black is komaster she can make ko to protect B2, but White gets 3 moves elsewhere.)

[Diagram]

Prevent sacrifice

After B1 Black gets 2 White stones plus 1 point of territory.



0.58 (7/12)

If B were komonster, it would be 0.75.



0.67 (2/3)

[Diagram]

Take away potential point, set up ko capture

[Diagram]

Defend potential point, set up ko capture

[Diagram]

Take stone to set up ko

Ambiguous.

[Diagram]

Make ko

[Diagram]

Take two stones

[Diagram]

Take away territory (i)

[Diagram]

Take away territory (ii)

[Diagram]

Take three stones



0.75

[Diagram]

Take away potential point (corridor)



0.83

[Diagram]

Defend potential point, set up 0.67 position

[Diagram]

Take away potential point

[Diagram]

Sente

Take stone in sente, leaving 0.67 point play.

[Diagram]

Reverse Sente

Save stone, leaving 0.5 point play.

[Diagram]

Protect, threaten 0.67 play



0.88

[Diagram]

Take away potential point (corridor)

$$ . . . . . . . .

[Diagram]

Take away potential point



0.94

[Diagram]

Take away potential point (corridor)



0.97

[Diagram]

Take away potential point (corridor)



For higher values see Miai Values List / 1.00 to 1.99, Miai Values List / 2.00 and more.


__ horizontal line (for ko): __

═ horizontal double line: ═


This is a copy of the living page "rubilia/NormalValues" at Sensei's Library.
(OC) 2004 the Authors, published under the OpenContent License V1.0.
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